It is likely common knowledge that I have a mixed reaction to Twitter. My common reaction after a Twitter session is that the feed is made up primarily of drivel and self or in-group promotion. I cannot understand even having tried from time to time how groups believe a Twitter chat offers the most meaningful way to interact.
However, having made my personal reactions clear, I obviously make some use of the service. I admit to constantly checking Twitter from my mobile devices. There is likely some useful information in this observation. I assume this is because I use my phone and often one of my tablets to skim. I can quickly thumb past the inane. What I tend to be looking for are links? I think I use Twitter as a discovery and not a learning tool. The discovery process is not sufficient for learning, but discovery does direct me toward content that may be useful. Perhaps there should be a way to hide any Tweet that does not contain a link.
Twitter, here is what I would suggest.. Create an internal mechanism for extended “posts”. You seem to have recognized the value of this strategy for images. Why not with other forms of multimedia content? I think it is fine that I can automatically forward a Tweet that links back to this content, but you may be missing out on an opportunity by allowing your users to do their real learning elsewhere.